Details

analyze43.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
62.4%	37.5%	0.1%	4
68.7%	31.2%	0.1%	5
68.7%	18.7%	12.6%	6
68.7%	17.2%	14.1%	7
68.7%	10.1%	21.2%	8
68.7%	9%	22.3%	9
68.7%	5.3%	26%	10
68.7%	4.6%	26.7%	11
68.7%	2.7%	28.6%	12
68.7%	2.3%	29%	13
68.7%	1.4%	30%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample751.0ms (23.9%)

Results

735.0ms	8256×	body	128	valid
3.0ms	34×	body	128	invalid

Compiler

Compiled 22 to 14 computations (36.4% saved)

preprocess16.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	10	26
0	2	2

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 10 to 6 computations (40% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	8	13

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 30 to 18 computations (40% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series31.0ms (1%)

Counts

2 → 48

Calls

12 calls:

5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))	b	inf
5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))	a	inf
5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))	b	-inf
5.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))	a	-inf
4.0ms	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))	a	0

rewrite47.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`log1p-expm1-u_binary64`
793×	`expm1-log1p-u_binary64`
485×	`prod-diff_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	21
1	147	21
2	2102	21

Stop Event

1×	node limit

Counts

2 → 70

simplify30.0ms (1%)

Algorithm

1×	egg-herbie

Rules

475×	`times-frac_binary64`
448×	`associate-+l+_binary64`
426×	`fma-def_binary64`
303×	`associate-/l*_binary64`
240×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	1020
1	334	981
2	1169	965

Stop Event

1×	node limit

Counts

118 → 100

prune112.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	97	4	101

Error

0.6b

Counts

101 → 4

Alt Table

Status	Error	Program
	1.2b	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	11.2b	(/.f64 1 (+.f64 1 (exp.f64 b)))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
▶	1.1b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))

Compiler

Compiled 2052 to 957 computations (53.4% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (exp.f64 a) 3)
✓	0.1b	(pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)
✓	0.3b	(/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3))
✓	0.4b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))

series169.0ms (5.4%)

Counts

4 → 76

Calls

21 calls:

27.0ms	(/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3))	a	0
24.0ms	(/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3))	b	0
19.0ms	(/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3))	b	inf
15.0ms	(/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3))	b	-inf
15.0ms	(/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3))	a	inf

rewrite60.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

560×	`prod-diff_binary64`
229×	`fma-def_binary64`
193×	`expm1-udef_binary64`
193×	`log1p-udef_binary64`
142×	`fma-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	49
1	232	46
2	3037	46

Stop Event

1×	node limit

Counts

4 → 141

simplify64.0ms (2%)

Algorithm

1×	egg-herbie

Rules

541×	`fma-def_binary64`
395×	`associate-/l*_binary64`
393×	`times-frac_binary64`
299×	`associate-/r*_binary64`
193×	`associate-*r/_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	464	4191
1	1757	4086

Stop Event

1×	node limit

Counts

217 → 195

prune183.0ms (5.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	195	4	199

Error

0.6b

Counts

199 → 4

Alt Table

Status	Error	Program
▶	1.2b	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	11.2b	(/.f64 1 (+.f64 1 (exp.f64 b)))
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	1.1b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))

Compiler

Compiled 7670 to 4383 computations (42.9% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	0.0b	(cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))
✓	0.4b	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))

series511.0ms (16.3%)

Counts

2 → 48

Calls

12 calls:

140.0ms	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)	a	0
43.0ms	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)	a	-inf
42.0ms	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)	a	inf
41.0ms	(pow.f64 (cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))) 3)	b	inf
38.0ms	(cbrt.f64 (/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b))))	a	0

rewrite49.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`prod-diff_binary64`
455×	`log-prod_binary64`
191×	`fma-def_binary64`
169×	`expm1-udef_binary64`
169×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	28
1	208	28
2	2596	28

Stop Event

1×	node limit

Counts

2 → 85

simplify99.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

901×	`fma-def_binary64`
307×	`*-commutative_binary64`
245×	`sqr-pow_binary64`
213×	`unswap-sqr_binary64`
192×	`associate-/r*_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	783	8369
1	2823	8243

Stop Event

1×	node limit

Counts

133 → 119

prune270.0ms (8.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	218	1	219
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	220	3	223

Error

0.6b

Counts

223 → 3

Alt Table

Status	Error	Program
▶	11.5b	(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) 3)
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	1.1b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))

Compiler

Compiled 12840 to 8499 computations (33.8% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 b))
✓	0.0b	(/.f64 1 (+.f64 1 (exp.f64 b)))
✓	0.0b	(cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))
✓	0.6b	(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) 3)

series146.0ms (4.6%)

Counts

4 → 32

Calls

12 calls:

31.0ms	(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) 3)	b	-inf
31.0ms	(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) 3)	b	inf
28.0ms	(cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))	b	-inf
27.0ms	(cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b))))	b	inf
16.0ms	(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) 3)	b	0

rewrite52.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

711×	`log1p-expm1-u_binary64`
711×	`expm1-log1p-u_binary64`
133×	`expm1-udef_binary64`
133×	`log1p-udef_binary64`
131×	`egg-rr`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	35
1	186	35
2	2032	35

Stop Event

1×	node limit

Counts

4 → 131

simplify39.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

782×	`times-frac_binary64`
389×	`fma-def_binary64`
291×	`associate-r_binary64`
259×	`cancel-sign-sub-inv_binary64`
235×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	91	550
1	265	542
2	883	520
3	4160	520

Stop Event

1×	node limit

Counts

163 → 132

prune97.0ms (3.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	131	4	135

Error

0.6b

Counts

135 → 4

Alt Table

Status	Error	Program
	11.9b	(pow.f64 (pow.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 b)) -1/2)) 2) 3)
✓	11.5b	(pow.f64 (cbrt.f64 (/.f64 1 (+.f64 1 (exp.f64 b)))) 3)
✓	0.8b	(/.f64 (exp.f64 a) (+.f64 (exp.f64 a) (exp.f64 b)))
✓	1.1b	(cbrt.f64 (/.f64 (pow.f64 (exp.f64 a) 3) (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))

Compiler

Compiled 2020 to 1608 computations (20.4% saved)

regimes271.0ms (8.6%)

Accuracy

Total 0.4b remaining (53.3%)

Threshold costs 0.4b (53.3%)

Counts

57 → 1

Compiler

Compiled 6121 to 4362 computations (28.7% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-rgt-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	15
1	18	15
2	22	15
3	24	15
4	25	15

Stop Event

1×

saturated

end63.0ms (2%)

Stop Event

1×

fuel

Compiler

Compiled 71 to 55 computations (22.5% saved)

Details

analyze43.0ms (1.4%)

sample751.0ms (23.9%)

preprocess16.0ms (0.5%)

simplify7.0ms (0.2%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series31.0ms (1%)

rewrite47.0ms (1.5%)

simplify30.0ms (1%)

prune112.0ms (3.6%)

localize8.0ms (0.3%)

series169.0ms (5.4%)

rewrite60.0ms (1.9%)

simplify64.0ms (2%)

prune183.0ms (5.8%)

localize7.0ms (0.2%)

series511.0ms (16.3%)

rewrite49.0ms (1.6%)

simplify99.0ms (3.2%)

prune270.0ms (8.6%)

localize6.0ms (0.2%)

series146.0ms (4.6%)

rewrite52.0ms (1.6%)

simplify39.0ms (1.3%)

prune97.0ms (3.1%)

regimes271.0ms (8.6%)

simplify2.0ms (0.1%)

end63.0ms (2%)

Profiling